A group invariant for links in thickened closed orientable surfaces is studied. Associated polynomial invariants are defined. The group detects nontriviality of a virtual link and determines its virtual genus....
It is known that the first two-variable Links--Gould quantum link invariant $LG\equiv LG^{2,1}$ is more powerful than the HOMFLYPT and Kauffman polynomials, in that it distinguishes all prime knots (including reflections) of up to 10 crossings. Her...
We study regularity properties of solutions to operator equations on patchwise smooth manifolds $\partialΩ$ such as, e.g., boundaries of polyhedral domains $Ω\subset \mathbb{R}^3$. Using suitable biorthogonal wavelet bases $Ψ$, we introduce a new...
We classify affine rank three Tits arrangements whose roots are contained in the locus of a homogeneous cubic polynomial. We find that there exist irreducible affine Tits arrangements which are not locally spherical....
An NP-complete coloring or homomorphism problem may become polynomial time solvable when restricted to graphs with degrees bounded by a small number, but remain NP-complete if the bound is higher. For instance, 3-colorability of graphs with degrees b...
Let G(V,E) be a simple graph and let X subset of V. Two vertices u and v are said to be X-visible if there exists a shortest u,v-path P such that V(P) intersection X is a subset of {u, v}. A set X is called a mutual-visibility set of G if every pair...
Mutual-visibility sets were motivated by visibility in distributed systems and social networks, and intertwine with several classical mathematical areas. Monotone properties of the variety of mutual-visibility sets, and restrictions of such sets to c...
Polyfill for `:focus-visible` (⭐ 1605)
Albert Visser has shown that Robinson's $ \mathsf{Q} $ and Gregorczyk's $ \mathsf{TC} $ are not sequential by showing that these theories are not even poly-pair theories, which, in a strong sense, means these theories lack pairing. In this paper, we...
Colorectal cancer is among the most common malignancies and can develop from high-risk colon polyps. Colonoscopy is an effective screening tool to detect and remove polyps, especially in the case of precancerous lesions. However, the missing rate in...
We present a special class of examples of automorphic lifts of multiple tensor products of automorphic representations, motivated by combinatorial identities for Schur polynomials and a celebrated result of Newton and Thorne....
We prove a highly uniform version of the prime number theorem for a certain class of $L$-functions. The range of $x$ depends polynomially on the analytic conductor, and the error term is expressed in terms of an optimization problem depending explici...
We give a review of results on the minimum convex cover and maximum hidden set problems. In addition, we give some new results. First we show that it is NP-hard to determine whether a polygon has the same convex cover number as its hidden set number....
In this note we point out the relation between Brion's formula for the lattice point generating function of a convex polytope in terms of the vertex cones [Brion1988] on the one hand, and the polar decomposition à la Lawrence/Varchenko [Lawrence19...
We generalize an inequality for convex lattice polygons -- aka toric surfaces -- to general rational surfaces....
This report defines (plain) Dag-like derivations in the purely implicational fragment of minimal logic $M_{\supset}$. Introduce the horizontal collapsing set of rules and the algorithm {\bf HC}. Explain why {\bf HC} can transform any polynomial heigh...
This paper explores a new version of the Levenberg-Marquardt algorithm used for Tensor Canonical Polyadic (CP) decomposition with an emphasis on image compression and reconstruction. Tensor computation, especially CP decomposition, holds significant...
Tea is the most popular drink on the planet (apart from water), with an estimated three cups consumed globally for every one of coffee. In the UK, however, tastes are shifting. According to the most recent figures, 63 per cent of UK adults regularly drink coffee, compared with 59…
Is it OK to go a little nuts over pistachios? Here’s what happens when you make these nutritional powerhouses part of your eating routine.
We address the black-box polynomial identity testing (PIT) problem for non-commutative polynomials computed by $+$-regular circuits, a class of homogeneous circuits introduced by [AJMR](STOC 2017, Theory of Computing 2019). These circuits can compute...